A swarm of 70 people is occupying Tate Modern's Turbine Hall. They walk slowly, solemnly, expressionlessly up the great ramp that leads to the west entrance of the museum. Or, if you arrive at another time, you might see them striding purposefully, or sprinting, or playing some mysterious running game as if chasing an invisible ball, or singing.

A young bearded man detaches himself from the group. He looks me in the eye and starts telling a story, about how he lived in Britain for seven years without once returning to his homeland, and when he finally did, and the plane touched down at the airport, he looked out of the window at the baggage handlers and the ground staff and realised with a shock that everyone looked just like him. And then he started to convulse with uncontrollable weeping, so that even all the children on the plane started staring at him. His story of rupture, exile and return is oddly powerful, not least because he does not say where his homeland is.

This is the new work for the Turbine Hall – a vast stage set that has, over the past dozen years, been the scene of Bruce Nauman's soundscapes, Olafur Eliasson's swollen orange sun and Doris Salcedo's chthonic rupture through the concrete floor. But These Associations, by the Anglo-German artist Tino Sehgal, is the first artwork here to use the intangible stuff of stories and personal interaction as its form – rather than sculpture, painting or installation.

London-born Sehgal, 36, who trained in political economy and dance in Berlin, where he is based, declines to make art that has a physical form. Previous works have included This Progress at the ICA, in which the visitor was greeted by a child, then conducted round the building by people of increasing age, while discussing the idea of progress. He also refuses to publish written explanations of his work or allow official photography although, in the age of the smartphone, plenty of informal pictures and films can be found on the internet.

For the millions of visitors who are expected to pass through Tate Modern's doors between Tuesday, when the work opens to the public, and 28 October, when it closes, the experience of being stopped and spoken to by a complete stranger may be uncomfortable. For Chris Dercon, the director of Tate Modern, it is "the most complex, difficult and dangerous project we have ever put into this museum".

According to Sehgal the work is about the relationship between the individual and the mass: "It is about what it means to belong to a group, which is also quite a personal question for me." The Turbine Hall was intriguing, he said, because "it is such an unusual space for a museum, since museums were invented to train visitors in polite behaviour. But the Turbine Hall is different: it is made to make people gather together and puts them in a joyful, bodily, unrestricted space."

Several hundred participants are involved in the project. They were recruited through networks of friends and acquaintances, and rehearsed by Sehgal and his producer, Asad Raza. The stories they tell visitors are based on a set of open-ended questions asked by Sehgal, such as: "When did you feel a sense of belonging?" and "When did you experience a sense of arrival?" The participants work in four-hour shifts, with breaks, and are paid, according to the Tate curator Jessica Morgan, between £8 and £9 per hour. Most are fitting the work at Tate around other professional commitments, from posts at universities to freelance photography.

According to Raza the work "shows London to itself; it is a more accurate picture of London than something that is cooked up by one particular person". On Monday morning though, none of the participants was black: according to Dercon, "we have complete diversity but we didn't select them as if we were casting a sitcom".

The Turbine Hall has a history of causing its visitors to behave in unexpected ways. Already, half an hour into the preview of the work, children were dashing about and imitating the participants' running games. According to Sehgal, "loss of control is something psychologically necessary to me. If it was all coming from me, it wouldn't be satisfactory."